Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

Optimal fuzzy PID control tuned with genetic algorithms

Fuzzy logic controllers (FLC) are intelligent systems, based on heuristic knowledge, that have been largely applied in numerous areas of everyday life. They can be used to describe a linear or nonlinear system and are suitable when a real system is not known or too difficult to find their model. FLC provide a formal methodology for representing, manipulating and implementing a human heuristic knowledge on how to control a system. These controllers can be seen as artificial decision makers that operate in a closed-loop system, in real time. The main aim of this work was to develop a single optimal fuzzy controller, easily adaptable to a wide range of systems – simple to complex, linear to nonlinear – and able to control all these systems. Due to their efficiency in searching and finding optimal solution for high complexity problems, GAs were used to perform the FLC tuning by finding the best parameters to obtain the best responses. The work was performed using the MATLAB/SIMULINK software. This is a very useful tool that provides an easy way to test and analyse the FLC, the PID and the GAs in the same environment. Therefore, it was proposed a Fuzzy PID controller (FL-PID) type namely, the Fuzzy PD+I. For that, the controller was compared with the classical PID controller tuned with, the heuristic Ziegler-Nichols tuning method, the optimal Zhuang-Atherton tuning method and the GA method itself. The IAE, ISE, ITAE and ITSE criteria, used as the GA fitness functions, were applied to compare the controllers performance used in this work. Overall, and for most systems, the FL-PID results tuned with GAs were very satisfactory. Moreover, in some cases the results were substantially better than for the other PID controllers. The best system responses were obtained with the IAE and ITAE criteria used to tune the FL-PID and PID controllers.

Fractional dynamics of a system with particles subjected to impacts

This paper studies the dynamics of a system composed of a collection of particles that exhibit collisions between them. Several entropy measures and different impact conditions of the particles are tested. The results reveal a Power Law evolution both of the system energy and the entropy measures, typical in systems having fractional dynamics.

Characterisation of adventitious lung sounds in people with dementia

Introduction: Lower Respiratory Tract Infections (LRTIs) are highly prevalent in institutionalised people with dementia, constituting an important cause of morbidity and mortality. Computerised auscultation of Adventitious Lung Sounds (ALS) has shown to be objective and reliable to assess and monitor respiratory diseases, however its application in people with dementia is unknown. Aim: This study characterised ALS (crackles and wheezes) in institutionalised people with dementia. Methods: An exploratory descriptive study, including 6 long-term care institutions was conducted. The sample included a dementia group (DG) of 30 people with dementia and a match healthy group (HG) of 30 elderly people. Socio-demographic and anthropometric data, cognition, type and severity of dementia, cardio-respiratory parameters, balance, mobility and activities and participation were collected. Lung sounds were recorded with a digital stethoscope following Computerised Respiratory Sound Analysis (CORSA) guidelines. Crackles’ location, number (N), frequency (F), two-cycle duration (2CD), initial deflection width (IDW) and largest deflection width (LDW) and wheezes’ number (N), ratio (R) and frequency (F) were analysed per breathing phase. Statistical analyses were performed using PASW Statistics(v.19). Results: There were no significant differences between the two groups in relation to the mean N of crackles during inspiration and expiration in both trachea and thorax. DG trachea crackles had significant higher F during inspiration and lower IDW, 2CD and LDW during expiration when compared with HG. At the thorax, the LDW during inspiration was also significantly lower in the DG. A significant higher N of inspiratory wheezes was found in the HG. Both groups had a low ratio of high frequency wheezes. Conclusion: Computerised analyses of ALS informed on the respiratory system and function of people with dementia and elderly people. Hence, this could be the step towards prevention, early diagnosis and continuous monitoring of respiratory diseases in people with cognitive impairment.

Numerical solution of a PDE system with non-linear steady state conditions that translates the air stripping pollutants removal

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.